Anna Beliakova

Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links

We define a family of formal Khovanov bracketsof a colored link depending on two param- eters. The isomorphismclassesof these bracketsare invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Fi- nally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levine-Tristram signature.

Trace decategorification of categorified quantum sl2

The trace or the 0th Hochschild–Mitchell homology of a linear category

Current algebras and categorified quantum groups

\mathcal {C}

A SIMPLIFICATION OF COMBINATORIAL LINK FLOER HOMOLOGY

C may be regarded as a kind of decategorification of

On the integrality of the Witten–Reshetikhin–Turaev 3-manifold invariants

\mathcal {C}

On the relation between two quantum group invariants of 3-cobordisms

C. We compute the traces of the two versions